Question: Nadia is 30 years older than Christopher. Thirteen years ago, Nadia was 4 times as old as Christopher. How old is Nadia now?
Answer: We can use the given information to write down two equations that describe the ages of Nadia and Christopher. Let Nadia's current age be $n$ and Christopher's current age be $c$ The information in the first sentence can be expressed in the following equation: $n = c + 30$ Thirteen years ago, Nadia was $n - 13$ years old, and Christopher was $c - 13$ years old. The information in the second sentence can be expressed in the following equation: $n - 13 = 4(c - 13)$ Now we have two independent equations, and we can solve for our two unknowns. Because we are looking for $n$ , it might be easiest to solve our first equation for $c$ and substitute it into our second equation. Solving our first equation for $c$ , we get: $c = n - 30$ . Substituting this into our second equation, we get the equation: $n - 13 = 4($ $(n - 30)$ $ -$ $ 13)$ which combines the information about $n$ from both of our original equations. Simplifying the right side of this equation, we get: $n - 13 = 4n - 172$ Solving for $n$ , we get: $3 n = 159$ $n = 53$.